Distributed estimation and detection for sensor networks using hidden Markov random field models (original) (raw)
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IEEE Transactions on Signal Processing, 2000
In large-scale wireless sensor networks, sensor-processor elements (nodes) are densely deployed to monitor the environment; consequently, their observations form a random field that is highly correlated in space. We consider a fusion sensor-network architecture where, due to the bandwidth and energy constraints, the nodes transmit quantized data to a fusion center. The fusion center provides feedback by broadcasting summary information to the nodes. In addition to saving energy, this feedback ensures reliability and robustness to node and fusion-center failures. We assume that the sensor observations follow a linear-regression model with known spatial covariances between any two locations within a region of interest. We propose a Bayesian framework for adaptive quantization, fusion-center feedback, and estimation of the random field and its parameters. We also derive a simple suboptimal scheme for estimating the unknown parameters, apply our estimation approach to the no-feedback scenario, discuss field prediction at arbitrary locations within the region of interest, and present numerical examples demonstrating the performance of the proposed methods.
Sensing capacity for markov random fields
Information Theory, 2005. ISIT …, 2005
AbstractThis paper computes the sensing capacity of a sensor network, with sensors of limited range, sensing a two-dimensional Markov random field, by modeling the sensing operation as an encoder. Sensor observations are dependent across sensors, and the sensor ...
We propose distributed methods for estimating and detecting the mean of a correlated Gaussian random eld observed by a sensor network. The random- field correlations are assumed to follow a conditional autoregressive (CAR) model. First, a distributed maximum likelihood (ML) estimator of the mean field is derived. We then develop batch and sequential detectors for testing the hypothesis that the mean field is greater than a specified level. We also derive exact and approximate performance measures for our methods. Numerical examples demonstrate the performance of the proposed approach.
Digital Signal Processing, 2014
We propose a new methodology for designing decentralized random field estimation schemes that takes the tradeoff between the estimation accuracy and the cost of communications into account. We consider a sensor network in which nodes perform bandwidth limited two-way communications with other nodes located in a certain range. The in-network processing starts with each node measuring its local variable and sending messages to its immediate neighbors followed by evaluating its local estimation rule based on the received messages and measurements. Local rule design for this two-stage strategy can be cast as a constrained optimization problem with a Bayesian risk capturing the cost of transmissions and penalty for the estimation errors. A similar problem has been previously studied for decentralized detection. We adopt that framework for estimation, however, the corresponding optimization schemes involve integral operators that are impossible to evaluate exactly, in general. We employ an approximation framework using Monte Carlo methods and obtain an optimization procedure based on particle representations and approximate computations. The procedure operates in a message-passing fashion and generates results for any distributions if samples can be produced from, e.g., the marginals. We demonstrate graceful degradation of the estimation accuracy as communication becomes more costly.
Spatial Sensor Selection via Gaussian Markov Random Fields
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2016
This paper addresses the problem of selecting the most informative sensor locations out of all possible sensing positions in predicting spatial phenomena by using a wireless sensor network. The spatial field is modelled by Gaussian Markov random fields (GMRF), where sparsity of the precision matrix enables the network to benefit from computation. A new spatial sensor selection criterion is proposed based on mutual information between random variables at selected locations and those at unselected locations and interested but unlikely sensor placed positions, which enhances resulting prediction. The GMRF based optimality criterion is then proven to be computationally and efficiently resolved, especially in a large-scale sensor network, by a polynomial time approximation algorithm. More importantly , with demonstrations of monotonicity and submodularity properties of the mutual information set function in the proposed selection criterion, our near-optimal solution is also guaranteed by at least within (1 − 1/e) of the optimal performance. The effectiveness of the proposed approach is compared and illustrated using two real-life large data sets with promising results.
Spatio-temporal random fields: compressible representation and distributed estimation
Machine Learning, 2013
Modern sensing technology allows us enhanced monitoring of dynamic activities in business, traffic, and home, just to name a few. The increasing amount of sensor measurements, however, brings us the challenge for efficient data analysis. This is especially true when sensing targets can interoperate-in such cases we need learning models that can capture the relations of sensors, possibly without collecting or exchanging all data. Generative graphical models namely the Markov random fields (MRFs) fit this purpose, which can represent complex spatial and temporal relations among sensors, producing interpretable answers in terms of probability. The only drawback will be the cost for inference, storing and optimizing a very large number of parameters-not uncommon when we apply them for real-world applications. In this paper, we investigate how we can make discrete probabilistic graphical models practical for predicting sensor states in a spatio-temporal setting. A set of new ideas allows keeping the advantages of such models while achieving scalability. We first introduce a novel alternative to represent model parameters, which enables us to compress the parameter storage by removing uninformative parameters in a systematic way. For finding the best parameters via maximal likelihood estimation, we provide a separable optimization algorithm that can be performed independently in parallel in each graph node. We illustrate that the prediction quality of our suggested methods is comparable to those of the standard MRFs and a spatio-temporal k-nearest neighbor method, while using much less computational resources.
Event-region estimation for sensor networks under the Poisson regime
2005
We develop a Bayesian method for event-region estimation in large-scale sensor networks under the Poisson regime. We propose a parametric model for the location and shape of the event region and assume that the unknown signal strength within this region is constant. We adopt a fusion architecture where each node in the network makes a decision locally and then conveys it to a fusion center. Both binary and quantized decisions are considered, corresponding to utilizing one or multiple thresholds (respectively) to make the local decisions. Markov chain Monte Carlo (MCMC) algorithms are derived for simulating from the posterior distributions of the unknown signal, location and shape parameters and for estimating these parameters. Numerical simulations demonstrate the performance of the proposed methods.
The embedded triangles algorithm for distributed estimation in sensor networks
IEEE Workshop on Statistical Signal Processing, 2003, 2003
We propose a new iterative distributed estimation algorithm for Gaussian hidden Markov graphical models with loops. We decompose a loopy graph into a number of linked ernbedded triangles and then apply a parallel block-lacohi iteration comprising local linear minimum mean-square-error estimation on each triangle (involving a simple 3 x 3 matrix inverse computation) followed by an information exchange between neighboring nodes and triangles. A simulation study demonstrates that the algorithm converges extremely rapidly, outperforming a number of existing algorithms. Embedded triangles are simple, local, scalable, fault-tolerant, and energy-efficient, and thus ideally suited for wireless sensor networks.
Efficient communication strategies for distributed signal field estimation
Asilomar Conference on Signals, Systems & Computers, 2004
Wireless sensor networks are a promising architecture for monitoring large spatial areas. While recent years have seen a surge of research activity in sensor networks, many significant challenges need to be overcome to realize the vision of sensor networks. The key challenges are tied to two vital operations in a sensor network: efficient information routing between sensor nodes to extract
Distributed maximum likelihood estimation in sensor networks
The problem of finding the maximum likelihood estimator of a commonly observed model, based on data collected by a sensor network under power and bandwidth constraints is considered. In particular, a case where the sensors cannot fully share their data is treated. An iterative algorithm that relaxes the requirement of sharing all the data is given. The algorithm is based on a local Fisher scoring method and an iterative information sharing procedure. The case where the sensors share sub-optimal estimates is also analyzed. The asymptotic distribution of the estimates is derived and used to provide means of discrimination between estimates that are associated with different local maxima of the loglikelihood function. The results are validated by a simulation.